Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices

We continue the study of Ambrosio and Serfaty (2008) [4] on the Chapman-Rubinstein-Schatzman-E evolution model for superconductivity, viewed as a gradient flow on the space of measures equipped with the quadratic Wasserstein structure. In Ambrosio and Serfaty (2008) [4] we considered the case of positive (probability) measures, while here we consider general real measures, as in the physical model. Understanding the evolution as a gradient flow in this context gives rise to several new questions, in particular how to define a “Wasserstein” distance for signed measures. We generalize the minimizing movement scheme of Ambrosio et al. (2005) [3] in this context, we show the entropy argument of Ambrosio and Serfaty (2008) [4] still carries through, and derive an evolution equation for the measure which contains an error term compared to the Chapman-Rubinstein-Schatzman-E model. Moreover, we also show the same applies to a very similar dissipative model on the whole plane.     

Vortices in the Maxwell‐Chern‐Simons theory

Our aim is to prove rigorously that the Chern‐Simons model of Hong, Kim, and Pac [13] and Jackiw and Weinberg [14] (the CS model) and the Abelian Higgs model of Ginzburg and Landau (the AH model, see [15]) are unified by the Maxwell‐Chern‐Simons theory introduced by Lee, Lee, and Min in [16] (MCS model). In [16] the authors give a formal argument that shows how to recover both the CS and AH models out of their theory by taking special limits for the values of the physical parameters involved. To make this argument rigorous, we consider the existence and multiplicity of periodic vortex solutions for the MCS model and analyze their asymptotic behavior as the physical parameters approach these limiting values. We show that, indeed, the given vortices approach (in a strong sense) vortices for the CS and AH models, respectively. For this purpose, we are led to analyze a system of two elliptic PDEs with exponential nonlinearities on a flat torus. © 2000 John Wiley & Sons, Inc.     

Assessing the predictive effectiveness of the variety seeking and reinforcement models

Prediction of customer choice behaviour has been a big challenge for marketing researchers. They have adopted various models to represent customers purchase patterns. Some researchers considered simple zero–order models. Others proposed higher–order models to represent explicitly customers tendency to seek [variety] or [reinforcement] as they make repetitive choices. Nevertheless, the question [Which model has the highest probability of representing some future data?] still prevails. The objective of this paper is to address this question. We assess the predictive effectiveness of the well–known customer choice models. In particular, we compare the predictive ability of the [dynamic attribute satiation] (DAS) model due to McAlister (Journal of Consumer Research, 91, pp. 141–150, 1982) with that of the well–known stochastic variety seeking and reinforcement behaviour models. We found that the stochastic [beta binomial] model has the best predictive effectiveness on both simulated and real purchase data. Using simulations, we also assessed the effectiveness of the stochastic models in representing various complex choice processes generated by the DAS. The beta binomial model mimicked the DAS processes the best. In this research we also propose, for the first time, a stochastic choice rule for the DAS model.     

Ultratopologies

The notion of ultratopologies was introduced in [6] motivated by the model theory of first and higher order logics. In [6] we established some model theoretical applications of ultratopologies, for example, we provided a purely set theoretical (or topological) characterization for classes de.nable by second order existential formulas. The present note deals with topological properties of ultratopologies, like density and compactness. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An optimal solution to a three echelon supply chain network with multi-product and multi-period

Recently, Kadadevaramath et al. (2012) [1] presented a mathematical model for optimizing a three echelon supply chain network. Their model is an integer linear programming (ILP) model. In order to solve it, they developed five algorithms; four of them are based on a particle swarm optimization (PSO) method and the other is a genetic algorithm (GA). In this paper, we develop a more general mathematical model that contains the model developed by Kadadevaramath et al. (2012) [1]. Furthermore, we show that all instances proved in Kadadevaramath et al. (2012) [1] can easily be solved optimally by any integer linear programming solver.     

A partial model of NF with ZF

The theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an axiom independent from NF (see also [12]). Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70.     

Convergence rate of solutions toward stationary solutions to a two-phase model with magnetic field in a half line

In this paper, we study an asymptotic behavior of a solution to the outflow problem for a two-phase model with magnetic field. Our idea mainly comes from [1] and [2] which investigate the asymptotic stability and convergence rates of stationary solutions to the outflow problem for an isentropic Navier–Stokes equation. For the two-phase model with magnetic field, we also obtain the asymptotic stability and convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method.     

Weights and Degrees in a Random Graph Model Based on 3-Interactions

In a random graph model introduced in [1] we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of the maximal weight and the maximal degree.     

Experiments with an interactive procedure for MOLP given weak orders on variables and objectives

In this paper we describe computational experiments with an interactive procedure for solving a multiobjective linear-programming model. The point of departure for this paper is the work described in Gass and Dror [4] and Dror and Gass [1] in which an interactive solution procedure is outlined. Here we describe improvements in the original procedure, as well as computational experiments, and demonstrate the procedure's ability to explore successfully the solution space of a multiobjective problem.     

Regularity of the solutions for micro-macro models near equilibrium

In this paper, we study the regularity of solutions to two microscopic-macroscopic models: Hookean spring model and FENE dumbbell model. By making use of the structure of Fokker-Planck operator and establishing the general Hardy-Littlewood's inequality, we show that the classical solutions near the equilibrium obtained in [F. Lin, C. Liu, Ping Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math. 60 (6) (2007) 838-866] and [F. Lin, Ping Zhang, The FENE dumbbell model near equilibrium, Acta Math. Sinica (Chin. Ser.) 24 (2008) 529-538] become smooth with respect to the end-to-end vector variable q for any positive time.     

The use of the bloomfield model as an approximation to ARMA processes in the context of fractional integration

In this article, we propose the use of a model proposed by Bloomfield [1] as an approximation to the ARMA structure underlying the I(0) disturbances in the context of fractional integration. For this purpose, we use tests due to Robinson [2] and show, via Monte Carlo simulations, that the power properties of the tests are not much affected by the use of this nonparametric approach. A small empirical application is also carried out at the end of the article.     

Double vortex condensates in the Chern-Simons-Higgs theory

For a selfdual model introduced by Hong-Kim-Pac [18] and Jackiw-Weinberg [19] we study the existence of double vortex-condensates“bifurcating” from the symmetric vacuum state as the Chern-Simons coupling parameter k tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as with the existence of extremal functions for a Sobolev inequality of the Moser-Trudinger's type on the flat 2-torus ([22], [1] and [15]). In fact, our construction yields to a “best” minimizing sequence for the (non-coercive) associated extremal problem, in the sense that, the infimum is attained if and only if the given minimizing sequence admits a convergent subsequence. Received: March 3, 1998 / Accepted October 23, 1998     

Exponential decay to a thermoelastic system with indefinite memory dissipation in a domain with moving boundary

We study the thermoelastic system in a domain with moving boundary, which was obtained when, instead of the Fourier’s law for the heat flux relation, we followed the linearized model proposed by Coleman and Gurtin [3] and Gurtin and Pipkin [6] about the memory theory of heat conduction. We show the existence, uniqueness and exponential decay rate of global regular solutions.     

Modelling Ziegler-Natta polymerization in high-pressure reactors

We present a study of some mechanical aspects of the polymerization processes named after the names of the Nobel laureates (1963) Karl W. Ziegler and Giulio Natta. Using the ideas of [1] as a starting point, we formulate a mathematical model encompassing the mechanical behavior of the polymer while it grows around the nanometric catalytic particles. As a basis we use the theory of [5]. The full model is exposed in [3]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Un modèle de Rotenberg avec des vitesses de maturité nulles

The Note [1] is devoted to the study of the Rotenberg's [8] model describing the growth of cell population when the maturation velocity belongs to a, b, with 0 < a < b < ∞. In this Note we bring new techniques for treating the case 0 = a < b < ∞.     

Compactness properties in the fuzzy real line

It is the purpose of this paper to give the solution to a number of open questions in [14], concerning the compactness properties of the fuzzy real line and the fuzzy real unit interval.However using the model of the fuzzy real line which we already proposed in [9, 12] we are able to describe all compactness properties not only of the spaces mentioned above but actually of several large classes of subspaces of the fuzzy real line; and thus the answers to the questions in [14] follow as easy consequences of our general results.     

Handling forecasting problems using fuzzy time series

In [6–9], Song et al. proposed fuzzy time-series models to deal with forecasting problems. In [10], Sullivan and Woodall reviewed the first-order time-invariant fuzzy time series model and the first-order time-variant model proposed by Song and Chissom [6–8], where the models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. In this paper, we propose a new method to forecast university enrollments, where the historical enrollments of the University of Alabama shown in [7,8] are used to illustrate the forecasting process. The average forecasting errors and the time complexity of these methods are compared. The proposed method is more efficient than the ones presented in [7, 8, 10] due to the fact that the proposed method simplifies the arithmetic operation process. Furthermore, the average forecasting error of the proposed method is smaller than the ones presented in [2, 7, 8].     

Zariski density in lie groups

In [7] Furstenberg gave a proof of Borel’s density theorem [1], which depended not on complete reducibility but rather on properties of the action of a minimally almost periodic group on projective space. In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groupsG and closed subgroupsH of cofinite volume. In [5] Dani gives a more general form of the density theorem in whichH need only be non-wandering. In the present paper we define the condition ofk-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize thek-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.     

On some riesz bases

In this paper we consider three problems concerning systems of vector exponentials. In the first part we prove a conjecture of V. Komornik raised in [14] on the independence of the movement of a rectangular membrane in different points. It was independently proved by M. Horváth [9] and S. A. Avdonin (personal communication). The analogous problem for the circular membrane was partly solved in [3] — the complete solution is given in [10]. In the second part we fill in a gap in the theory of Blaschke-Potapov products developed in the paper [19] of Potapov. Namely we prove that the Blaschke-Potapov product is determined by its kernel sets up to a multiplicative constant matrix. In the third part of the present paper we give a multidimensional generalization of the notion of sine type function developed by Levin [16], [17] and by our generalization we prove the multidimensional variant of the Levin-Golovin basis theorem [16], [6].     

Uniform persistence for a two-species ratio-dependent predator-prey system with diffusion and variable time delays

A two-species ratio-dependent predator-prey diffusion model with variable time delays is investigated. By constructing some suitable Lyapunov functionals and utilizing some analysis techniques, we obtain the permanence of this system. Our results generalize and improve the results of [10] and [11].